Narrow Results

We investigate the CP violating asymmetry, the forward backward asymmetry and the CP violating asymmetry in the forward–backward asymmetry for the inclusive B → X_dℓ⁺ℓ^- decays for the ℓ = e,μ,τ channels in the standard model. It is observed that these asymmetries are quite sizeable and B → X_dℓ⁺ℓ^- decays seem promising for investigating CP violation.

It is shown that in an axial-vector field theory the axial-vector field is always accompanied by a spin-0 field which has negative metric. Therefore, the theory has problem of negative probability and unitarity is broken. The same results are found in a theory of charged vector fields which are coupled to two fermions whose masses are different. These results are applied to the SM. It is found that both Z and W fields contain spin-0 component. Their masses are m_ϕ⁰ = m_te^28.4 = 3.78 × 10¹⁴ GeV and m_ϕ^± = m_te²⁷ = 9.31 × 10¹³ GeV respectively. A new perturbation theory of the SM is proposed. The propagators of Z and W fields in this new perturbation theory are derived in "unitary gauge." A minus sign is obtained in front of the scalar part of the propagators of W and Z fields. The minus sign indicates that the scalar fields have negative metric which leads to negative probability. Therefore, the unitarity of the SM is broken at about ~ 10¹⁴ GeV.

We study the resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$ in the perturbative QCD approach. The branching ratios for $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^{+}{K}^{-}$ and $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^0{\bar{K}}^0$ are predicted to be $(1.53\pm 0.23)\times 10^{-7}$ and $(1.02_{-0.13}^{+0.19})\times 10^{-7}$, respectively. The decay $B^{+}\to D_s^{+}\varphi (1680)$ with $\varphi (1680)$ decays into $K^{+}{K}^{-}$ or $K^0{\bar{K}}^0$, has the branching fraction $(6.94_{-2.02}^{+1.83})\times 10^{-9}$, which is about $5\%$ of the result for $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^{+}{K}^{-}$.